Why my results of regress function and fitlm function are different?

My code is:

clear all
clc
x=[1 2 3 4 5 6 7 8 9 10];
y=[4 5 2 7 2 8 10 2 1 5];

tbl = table(y' , x');
mdl = fitlm(tbl,'linear')


b = regress(y',[ones(size(x',1),1),x'])

I have added an intercept when operating regress function. But the results are still different.

Here are the results:

fitlm function:

mdl = 


Linear regression model:
    Var2 ~ 1 + Var1

Estimated Coefficients:
                   Estimate       SE         tStat       pValue 
                   _________    _______    _________    ________

    (Intercept)       5.6144     1.9347        2.902    0.019832
    Var1           -0.024876    0.35803    -0.069479     0.94631


Number of observations: 10, Error degrees of freedom: 8
Root Mean Squared Error: 3.21
R-squared: 0.000603,  Adjusted R-Squared: -0.124
F-statistic vs. constant model: 0.00483, p-value = 0.946

regress function

b =

    4.7333
   -0.0242

I'm wondering the reason of the difference. And I want to know when should I use fitlm or regress. Thanks!

Answer 1

[dpb]

I don't see that...I'm guessing a different y vector, somehow, maybe???

x=[1 2 3 4 5 6 7 8 9 10].';
y=[4 5 2 7 2 8 10 2 1 5].';
mdl=fitlm(x,y,'linear');
fliplr(mdl.Coefficients.Estimate.') 

ans = 1×2

-0.0242 4.7333

fliplr(regress(y,[ones(size(x)) x]).') 

ans = 1×2

-0.0242 4.7333

polyfit(x,y,1)

ans = 1×2

-0.0242 4.7333

[Yingjin Liu]

Thank you!

I checked your code and mine, then I found I set y' in the first column. Therefore, the result of fitlm was the regression of x~1+y. Now I see. When using regress command, it is regress(y,x). While using fitlm, it is fitlm(x,y).

[dpb]

I whiffed on the reversal when the variables were buried in the table reference for your model, sorry.

"...it is regress(y,x). While using fitlm, it is fitlm(x,y)."

Yes, this is another case where TMW created an unnecessary user confusion/chance for error such as here by having the oddball regression routine that doesn't match any of the others in the stable. It's just poor user interface design despite the theoretical statement that one "regresses y on x"; writing the input arguments in that order simply is completely inconsistent with all regression routines and so is user error bound to trap the unwary.